Add AVI to Blender Animation
as @DuarteFarrajotaRamos said in comments (and his answer to the linked question) it's a current limit in viewport implementation, and it should work when rendered.
While the animation, though the video will not be updated in the 3d viewport, you can click on the viewport (anywhere) to see the &quot;current&quot; frame. Not so useful, but it shows at least what is shown at that frame...
But there's a (silly) temporary workaround if you need to see that video really playing in the viewport: start playing the animation with the shortcut (ALTA) while hovering the mouse cursor in the right-side texture preview panel, like shown here (note: my screen capturing tool doesn't show the cursor, just the clicks):

so, if you need to see something, at least you have some way to go...